Borsuk-Ulam theorems for arbitrary 𝑆¹ actions and applications

Fadell, E. R.; Husseini, S. Y.; Rabinowitz, P. H.

doi:10.1090/S0002-9947-1982-0670937-0

Borsuk-Ulam theorems for arbitrary $S^{1}$ actions and applications
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by E. R. Fadell, S. Y. Husseini and P. H. Rabinowitz PDF

Trans. Amer. Math. Soc. 274 (1982), 345-360 Request permission

Abstract:

An ${S^1}$ version of the Borsuk-Ulam Theorem is proved for a situation where Fix ${S^1}$ may be nontrivial. The proof is accomplished with the aid of a new relative index theory. Applications are given to intersection theorems and the existence of multiple critical points is established for a class of functional invariant under an ${S^1}$ symmetry.

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